In this dissertation, first we consider the problem of testing homogeneity and order in a contaminated normal model, when the data is correlated under some known covariance structure. To address this problem, we developed a moment based homogeneity and order test, and design weights for test statistics to increase power for homogeneity test. We applied our test to microarray about Down’s syndrome. This dissertation also studies a singular Bayesian information criterion (sBIC) for a bivariate hierarchical mixture model with varying weights, and develops a new data dependent information criterion (sFLIC).We apply our model and criteria to birth- weight and gestational age data for the same model, whose purposes are to select model complexity from data.

Thesis (MSc)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: See full text for abstract / AFRIKAANSE OPSOMMING: Sien volteks vir opsomming

Spatial-temporal autologistic models are useful models for binary data that are measured repeatedly over time on a spatial lattice. They can account for effects of potential covariates and spatial-temporal statistical dependence among the data. However, the traditional parametrization of spatial-temporal autologistic model presents difficulties in interpreting model parameters across varying levels of statistical dependence, where its non-negative autocovariates could bias the realizations toward 1. In order to achieve interpretable parameters, a centered spatial-temporal autologistic regression model has been developed. Two efficient statistical inference approaches, expectation-maximization pseudo-likelihood approach (EMPL) and Monte Carlo expectation-maximization likelihood approach (MCEML), have been proposed. Also, Bayesian inference is considered and studied. Moreover, the performance and efficiency of these three inference approaches across various sizes of sampling lattices and numbers of sampling time points through both simulation study and a real data example have been studied. In addition, We consider the imputation of missing values is for spatial-temporal autologistic regression models. Most existing imputation methods are not admissible to impute spatial-temporal missing values, because they can disrupt the inherent structure of the data and lead to a serious bias during the inference or computing efficient issue. Two imputation methods, iteration-KNN imputation and maximum entropy imputation, are proposed, both of them are relatively simple and can yield reasonable results. In summary, the main contributions of this dissertation are the development of a spatial-temporal autologistic regression model with centered parameterization, and proposal of EMPL, MCEML, and Bayesian inference to obtain the estimations of model parameters. Also, iteration-KNN and maximum entropy imputation methods have been presented for spatial-temporal missing data, which generate reliable imputed values with the reasonable efficient imputation time.

In many areas of the agriculture, biological, physical and social sciences, spatial lattice data are becoming increasingly common. In addition, a large amount of lattice data shows not only visible spatial pattern but also temporal pattern (see, Zhu et al. 2005). An interesting problem is to develop a model to systematically model the relationship between the response variable and possible explanatory variable, while accounting for space and time effect simultaneously. Spatial-temporal linear model and the corresponding likelihood-based statistical inference are important tools for the analysis of spatial-temporal lattice data. We propose a general asymptotic framework for spatial-temporal linear models and investigate the property of maximum likelihood estimates under such framework. Mild regularity conditions on the spatial-temporal weight matrices will be put in order to derive the asymptotic properties (consistency and asymptotic normality) of maximum likelihood estimates. A simulation study is conducted to examine the finite-sample properties of the maximum likelihood estimates. For spatial data, aside from traditional likelihood-based method, a variety of literature has discussed Bayesian approach to estimate the correlation (auto-covariance function) among spatial data, especially Zheng et al. (2010) proposed a nonparametric Bayesian approach to estimate a spectral density. We will also discuss nonparametric Bayesian approach in analyzing spatial data. We will propose a general procedure for constructing a multivariate Feller prior and establish its theoretical property as a nonparametric prior. A blocked Gibbs sampling algorithm is also proposed for computation since the posterior distribution is analytically manageable.

Given the increase in popularity of Lifetime Value (LTV), the argument is that the topic will assume an increasingly central role in research and marketing. As such, the decision to assess the state of the field in Lifetime Value Modelling, and outline challenges unique to choice researchers in customer relationship management (CRM). As the research has argued, there are an excess of issues and analytical challenges that remain unresolved. The researcher hopes that this thesis inspires new answers and new approaches to resolve LTV. The scope of this project covers the building of a LTV model through multiple regression. This thesis is exclusively focused on modelling tenure. In this regard, there are a variety of benchmark statistical techniques arising from survival analysis, which could be applied, to tenure modelling. Tenure prediction will be looked at using survival analysis and compared with "crossbreed" data mining techniques that use multiple regression in concurrence with statistical techniques. It will be demonstrated how data mining tools complement the statistical models, and show that their mutual usage overcomes many of the shortcomings of each singular tool set, resulting in LTV models that are both accurate and comprehensible. Bank XYZ is used as an example and is based on a real scenario of one of the Banks of South Africa. / Thesis (M.Sc. (Computer Science))--North-West University, Vaal Triangle Campus, 2009.

Within NASA's Air Traffic Management Technology Demonstration # 1 (ATD-1), Interval Management (IM) is a flight deck tool that enables pilots to achieve or maintain a precise in-trail spacing behind a target aircraft. Previous research has shown that violations of aircraft spacing requirements can occur between an IM aircraft and its surrounding non-IM aircraft when it is following a target on a separate route. This research focused on the experimental design and analysis of a deterministic computer simulation which models our airspace configuration of interest. Using an original space-filling design and Gaussian process modeling, we found that aircraft delay assignments and wind profiles significantly impact the likelihood of spacing violations and the interruption of IM operations. However, we also found that implementing two theoretical advancements in IM technologies can potentially lead to promising results.

The following dissertation contains two distinct empirical essays which contribute to the overall field of Financial Economics. Chapter 1, entitled “The Determinants of Dynamic Dependence: An Analysis of Commodity Futures and Equity Markets,” examines the determinants of the dynamic equity-commodity return correlations between five commodity futures sub-sectors (energy, foods and fibers, grains and oilseeds, livestock, and precious metals) and a value-weighted equity market index (S&P 500). The study utilizes the traditional DCC model, as well as three time-varying copulas: (i) the normal copula, (ii) the student’s t copula, and (iii) the rotated-gumbel copula as dependence measures. Subsequently, the determinants of these various dependence measures are explored by analyzing several macroeconomic, financial, and speculation variables over different sample periods. Results indicate that the dynamic equity-commodity correlations for the energy, grains and oilseeds, precious metals, and to a lesser extent the foods and fibers, sub-sectors have become increasingly explainable by broad macroeconomic and financial market indicators, particularly after May 2003. Furthermore, these variables exhibit heterogeneous effects in terms of both magnitude and sign on each sub-sectors’ equity-commodity correlation structure. Interestingly, the effects of increased financial market speculation are found to be extremely varied among the five sub-sectors. These results have important implications for portfolio selection, price formation, and risk management. Chapter 2, entitled, “US Community Bank Failure: An Empirical Investigation,” examines the declining, but still pivotal role, of the US community banking industry. The study utilizes survival analysis to determine which accounting and macroeconomic variables help to predict community bank failure. Federal Deposit Insurance Corporation and Federal Reserve Bank data are utilized to compare 452 community banks which failed between 2000 and 2013, relative to a sample of surviving community banks. Empirical results indicate that smaller banks are less likely to fail than their larger community bank counterparts. Additionally, several unique bank-specific indicators of failure emerge which relate to asset quality and liquidity, as well as earnings ratios. Moreover, results show that the use of the macroeconomic indicator of liquidity, the TED spread, provides a substantial improvement in modeling predictive community bank failure.

Neste trabalho desenvolveremos um modelo estatístico em uma escala micrométrica de interações entre as componentes do sistema que pretende descrever a propagação de trincas em materiais submetidos a tensões cíclicas. Apesar de sua extrema simplicidade, este modelo é capaz de reproduzir um resultado experimental bastante difundido entre engenheiros e especialistas, conhecido como lei de Paris, cujo enunciado estabelece que a taxa de crescimento de uma trinca sob carregamento cíclico é proporcional a uma potência da variação em seu correspondente fator de intensidade de tensões sendo largamente utilizada em aplicações práticas. Estamos particularmente interessados em estudar a introdução de desordem em determinados parâmetros associados ao material investigando as modificações impostas por este tipo de abordagem ao comportamento estatístico do modelo. Nossos principais resultados serão obtidos numericamente a partir de uma aproximação do tipo campo efetivo que ignora a correlação existente entre as diversas trincas que podem se formar ao longo do sistema durante o processo. Simulações numéricas do modelo serão igualmente consideradas ao analisarmos situações mais gerais do processo de propagação em que efeitos associados à regeneração de trincas podem desempenhar um importante papel na descrição do comportamento mecânico de um material. / In this work we consider a statistical model in a micrometric scale of interactions between the components of the system which intends to describe the failure of materials subjected to cyclic-load fatigue. Although quite simple, this model is able to reproduce an important experimental result widespread among engineers and experts, known as Paris law, which states that the growth rate of a crack at subcritical load is proportional to a power of the change in its stress-intensity factor and it is largely used in engineering practice. We are particularly interested to study the introduction of disorder in some parameters of the material investigating the modifications caused by this kind of approach in the statistical properties of the model. Our main results will be obtained numerically assuming an effective-field like approximation which neglects the correlation between the different cracks emerging throughout the system during the breaking process. Numerical simulations of the model are also performed in order to describe more general situations of propagation where the effects of crack self-healing can play an important role in the material strength.

A associação entre latitude e o tamanho corporal dos seres vivos é um fenômeno discutido por muitos pesquisadores. Foi observado que os corpos tendem a ser maiores em locais mais distantes do Equador e a temperatura ambiental já foi considerada a causa principal desse aumento corporal. O objetivo geral deste trabalho é verificar a relação entre altura e variáveis climáticas no Brasil, seguido dos objetivos específicos: i) construir cartogramas representativos das variáveis climáticas no Brasil; ii) verificar a existência de relação entre altura e latitude na população brasileira; iii) determinar, utilizando métodos estatísticos, quais elementos climáticos influenciam no crescimento das pessoas e iv) discutir a influência da sazonalidade dos elementos climáticos nas respostas fisiológicas do organismo humano. Para contemplar os objetivos colocados, este trabalho utilizou dados antropométricos, geográficos e climáticos previamente publicados por institutos de pesquisa brasileiros para investigar a existência e possíveis causas da correlação entre latitude e estatura de adolescentes de 12 anos de idade do sexo feminino e 14 anos de idade do sexo masculino. A variação latitudinal é seguida pela variação de diversos elementos climáticos, os aqui estudados foram: temperatura, insolação, radiação solar global e duração efetiva do dia. Os modelos matemáticos e de regressão linear múltipla mostram que o peso corporal juntamente a alguma variável climática são os melhores estimadores da estatura nas idades analisadas e a duração efetiva do dia acima de determinada intensidade luminosa é a variável climática que mais vezes mostrou-se estatisticamente relevante. Uma resposta para a existência da variação clinal na estatura dos seres humanos pode estar relacionada com a influência ambiental, que é dada em função da localização geográfica e da sazonalidade sobre a fisiologia humana. / The association between latitude and body size of living beings is a phenomenon discussed by many researchers. It was observed that the bodies tend to be larger in places more distant from the Equator and the environmental temperature has already been considered the main cause of this corporal increase. The general objective of this work is to verify the relationship between height and climatic variables in Brazil, followed by the specific objectives: i) to construct cartograms representative of climatic variables in Brazil; ii) verify the existence of a relationship between height and latitude in the Brazilian population; iii) determine, using statistical methods, which climatic elements influence the growth of people, and iv) discuss the seasonal influence of climatic elements on the physiological responses of the human organism. In order to contemplate the objectives, this work used anthropometric, geographic and climatic data previously published by Brazilian research institutes to investigate the existence and possible causes of the correlation between latitude and height of 12-year-old female and 14-year-old adolescents male. The latitudinal variation is followed by the variation of several climatic elements, the ones studied here were: temperature, insolation, global solar radiation and effective day length. The mathematical and multiple linear regression models show that body weight together with some climatic variable are the best height estimators in the analyzed ages and the effective day length above a determined luminous intensity is the climatic variable that has shown to be statistically more relevant . An answer for the existence of clinal variation in human stature may be related to environmental influence, which is given by geographic location and seasonality on human physiology

Neste trabalho desenvolveremos um modelo estatístico em uma escala micrométrica de interações entre as componentes do sistema que pretende descrever a propagação de trincas em materiais submetidos a tensões cíclicas. Apesar de sua extrema simplicidade, este modelo é capaz de reproduzir um resultado experimental bastante difundido entre engenheiros e especialistas, conhecido como lei de Paris, cujo enunciado estabelece que a taxa de crescimento de uma trinca sob carregamento cíclico é proporcional a uma potência da variação em seu correspondente fator de intensidade de tensões sendo largamente utilizada em aplicações práticas. Estamos particularmente interessados em estudar a introdução de desordem em determinados parâmetros associados ao material investigando as modificações impostas por este tipo de abordagem ao comportamento estatístico do modelo. Nossos principais resultados serão obtidos numericamente a partir de uma aproximação do tipo campo efetivo que ignora a correlação existente entre as diversas trincas que podem se formar ao longo do sistema durante o processo. Simulações numéricas do modelo serão igualmente consideradas ao analisarmos situações mais gerais do processo de propagação em que efeitos associados à regeneração de trincas podem desempenhar um importante papel na descrição do comportamento mecânico de um material. / In this work we consider a statistical model in a micrometric scale of interactions between the components of the system which intends to describe the failure of materials subjected to cyclic-load fatigue. Although quite simple, this model is able to reproduce an important experimental result widespread among engineers and experts, known as Paris law, which states that the growth rate of a crack at subcritical load is proportional to a power of the change in its stress-intensity factor and it is largely used in engineering practice. We are particularly interested to study the introduction of disorder in some parameters of the material investigating the modifications caused by this kind of approach in the statistical properties of the model. Our main results will be obtained numerically assuming an effective-field like approximation which neglects the correlation between the different cracks emerging throughout the system during the breaking process. Numerical simulations of the model are also performed in order to describe more general situations of propagation where the effects of crack self-healing can play an important role in the material strength.